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Grants





Qualitative analysis and numerical solution of flow problems (201/08/0012)
from 01/01/2008
to 31/12/2012 main investigator

Objectives:
Mathematical modelling of fluid flows in different regimes.



Mathematical analysis of complex systems in the fluid mechanics (201/08/0315)
from 01/01/2008
to 31/12/2011 investigator

The main goal of the project is to develop a rigorous mathematical theory of complex systems in fluid mechanics. Such problems arise in models of chemical reactions, astrophysics, biological models, atmosphere and geophysical fluid dynamics. The main challenge here is to handle problems with large data and without any restriction concerning the time scale. The main topics include: Multicomponent problems and mixtures. 2. Equations of magnetohydrodynamics. 3. Atmospheric and geophysical models. 4. Large time behavior of solutions and equilibrium states.



Nečas Center for Mathematical Modeling  part IM (LC06052)
from 01/01/2006
to 31/12/2011 investigator

The general goal of the Nečas Center for Mathematical Modeling is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of five important research teams at three Prague affiliations and their goaldirected collaboration with top experts from abroad. The research projects of the center include: 1) Nonlinear theoretical, numerical and computer analysis of problems of continuum physics. 2) Heatconductive and deforming processes in compressible fluids, incompressible substances of fluid type, and in linearly elastic matters. 3) Interaction of the substances. 4) Biochemical procedures in substances. 5) Passages between models, dimensional analysis.



Mathematical analysis in the thermodynamics of fluids (201/05/0164)
from 01/01/2005
to 30/12/2007 investigator

The aim of the present research project is to establish a coherent mathematical theory of viscous heat conducting fluids based on a suitable variational formulation of the problem consistent with the second law of thermodynamics. The main topics include: 1. The existence of solutions on arbitrarily large time intervals with no restriction on the size of data. 2. The questions of uniqueness, boundedness, and stability of solutions with respect to the initial conditions and other parameters as the case may be. 3. The long time behavior, convergence towards equilibria, and attractors. 4. Sensitivity analysis with respect to the shape of the underlying spatial domain.



Mathematical theory and numerical simulation of problems in the fluid mechanics (201/05/0005)
from 01/01/2005
to 31/12/2007 main investigator

The goal of this project is to investigate various models of the fluid mechanics from the theoretiacl point of view (exitence, uniqueness, regularity) and to use the theoretical results to improving various numerical methods in the fluid flow modeling.



Mathematical and numerical analysis of problems in fluid mechanics (201/02/0684)
from 01/01/2002
to 31/12/2004 main investigator

The project includes several topics: 1) Regularity of weak solutions to the NavierStokes equations. 2) Existence, stability and long time behaviour of solutions to compressible NavierStokes equations. 3) Interaction of fluids with rigid bodies. 4) Qualitative theory of higherdegree fluids. 5) Higher order schemes for compressible flows. 6) Adaptive methods of mesh refinement near discontinuities. 7) Extensions of finite volume  finite element methods from 2D to 3D problems.
